I think this assumes a more efficient rental market than what actually exists. Even in highly demand-skewed some properties sit empty for weeks/months between tenants.
> this will simply increase incentive to sell (if you can’t get enough to rent out), reducing the purchase price, and allowing people to live there.
But that means less supply for rental, and presumably lower impact on the demand for rental given how different the renting versus buying populations are. Even in a maximally efficient model this should result in raising rents?